Updating the banner (#10609)

For 3.22.  As it says.

---------

Co-authored-by: Parker Lougheed <parlough@gmail.com>

src/_includes/banner.html

@@ -2,7 +2,8 @@
   For headings use h3 elements.
 {% endcomment -%}
 <div class="site-banner site-banner--default" role="alert">
-  Flutter is back at Google I/O on May 14!
-  <a href="https://io.google/2024/?utm_source=flutter&utm_medium=embedded_marketing" target="_blank">Watch the livestream!</a>
+  Flutter 3.22 is live! Check out the <a href="https://medium.com/flutter/io24-5e211f708a37">Flutter 3.22 and Dart 3.4</a> announcement,<br>
+  the <a href="https://medium.com/flutter/whats-new-in-flutter-3-22-fbde6c164fe3">3.22 technical</a> blog post.<br>
+  Also check out <a href="/release/whats-new">what's new</a> on the website.
 </div>